Find the sum of N terms of the series 12, 14, 24, 58, 164, …

Given a positive integer, N. Find the sum of the first N term of the series 12, 14, 24, 58, 164, …..

Examples:

Input: N = 5
Output: 272

Input: N = 3
Output: 50

Approach: 

The sequence is formed by using the following pattern. For any value N-

S_N = 3^N – N² + 11 * N – 1

Illustration:

Input: N = 5
Output: 272
Explanation:
S_N = 3^N – N² + 11 * N – 1
     = 3⁵ – 5² + 11 * 5 – 1
     = 243 – 25 + 54
     = 272

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to return sum of
// N term of the series
int findSum(int N)
{
    return (pow(3, N) -
            pow(N, 2) +
            11 * N - 1);
}

// Driver Code
int main()
{
    int N = 5;
    cout << findSum(N);
    return 0;
}

Java

// Java program to implement
// the above approach
class GFG {

    // Function to return sum of
    // N term of the series
    static int findSum(int N) {
        return (int) (Math.pow(3, N) - Math.pow(N, 2) + 11 * N - 1);
    }

    // Driver Code
    public static void main(String args[]) {
        int N = 5;
        System.out.print(findSum(N));
    }
}

// This code is contributed by saurabh_jaiswal.

Python3

# Python code for the above approach

# Function to return sum of
# N term of the series
def findSum(N):
    return ((3 ** N) -
        (N ** 2) +
        11 * N - 1);

# Driver Code

# Get the value of N
N = 5;
print(findSum(N));

# This code is contributed by Saurabh Jaiswal

C#

// C# program to implement
// the above approach
using System;
class GFG
{

  // Function to return sum of
    // N term of the series
    static int findSum(int N) {
        return (int) (Math.Pow(3, N) - Math.Pow(N, 2) + 11 * N - 1);
    }

  // Driver Code
  public static void Main()
  {
    int N = 5;
    Console.Write(findSum(N));

  }
}

// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
        // JavaScript code for the above approach

        // Function to return sum of
        // N term of the series
        function findSum(N) {
            return (Math.pow(3, N) -
                Math.pow(N, 2) +
                11 * N - 1);
        }
        // Driver Code

        // Get the value of N
        let N = 5;
        document.write(findSum(N));

  // This code is contributed by Potta Lokesh
    </script>

Output

272

Time Complexity: O(logN) since it is using pow function

Auxiliary Space: O(1), since no extra space has been taken.